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Unformatted text preview: ECON 4261: Introduction to Econometrics Fall 2009 Problem Set 2 Due: Oct 22, 2009 Exercise 1 Suppose you model a variable Y depending on a non-stochastic variable X , according to the relation Y i = X i + u i . The disturbance terms are iid with mean zero and variance 2 . Considering estimating by the slope of a line between the origin and one out of the n plotted observations ( X i ,Y i ) . (a) Is this estimator unbiased? (b) Find the variance of this estimator. (c) Which of the observations would you choose to calculate the estimate? Justify your answer. Exercise 2 You are given 30 pairs of observations ( X i ,Y i ) which are to be represented by the following model Y i = + 1 X i + u i , and the errors are iid with mean zero and variance 2 . Suppose you know that R 2 = 0 . 25, n i =1 ( X i- X ) 2 = 49 and n i =1 ( Y i- Y ) 2 = 49. Calculate the OLS estimate for 1 (assume is positive)....
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